Aim: stores an arbitrary measure on a SurfaceMesh object. The measure can be spread onto its vertices, edges, or faces. This class is notably used by CorrectedNormalCurrentComputer and NormalCycleComputer to store the curvature measures, which may be located on different cells. The measure can be scalar or any other summable type (see template parameter TValue). More...

#include <DGtal/geometry/meshes/SurfaceMeshMeasure.h>

Inheritance diagram for DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >:

[legend]

Public Types
typedef TRealPoint	RealPoint
typedef TRealVector	RealVector
typedef TValue	Value
typedef SurfaceMeshMeasure< RealPoint, RealVector, Value >	Self
typedef DGtal::SurfaceMesh< RealPoint, RealVector >	SurfaceMesh
typedef SurfaceMesh::Index	Index
typedef SurfaceMesh::Size	Size
typedef SurfaceMesh::Vertex	Vertex
typedef SurfaceMesh::Edge	Edge
typedef SurfaceMesh::Face	Face
typedef std::vector< Value >	Values
typedef RealVector::Component	Scalar
typedef std::pair< Face, Scalar >	WeightedFace
typedef std::pair< Edge, Scalar >	WeightedEdge
typedef std::pair< Vertex, Scalar >	WeightedVertex
typedef std::vector< Vertex >	Vertices
	The type that defines a range of vertices.
typedef std::vector< Edge >	Edges
	The type that defines a range of edges.
typedef std::vector< Face >	Faces
	The type that defines a range of faces.
typedef std::vector< WeightedVertex >	WeightedVertices
typedef std::vector< WeightedEdge >	WeightedEdges
typedef std::vector< WeightedFace >	WeightedFaces

Public Member Functions
Standard services (construction, initialization, assignment)
	SurfaceMeshMeasure (ConstAlias< SurfaceMesh > aMesh=nullptr, Value zero_value=Value())
const SurfaceMesh *	meshPtr () const
const Values &	kMeasures (Dimension dim) const
Values &	kMeasures (Dimension dim)
Measure services
Value	measure () const
Value	measure (const RealPoint &x, Scalar r, Face f) const
Value	vertexMeasure (Vertex v) const
Value	vertexMeasure (const Vertices &vertices) const
Value	vertexMeasure (const WeightedVertices &wvertices) const
Value	edgeMeasure (Edge e) const
Value	edgeMeasure (const Edges &edges) const
Value	edgeMeasure (const WeightedEdges &wedges) const
Value	faceMeasure (Face f) const
Value	faceMeasure (const Faces &faces) const
Value	faceMeasure (const WeightedFaces &wfaces) const

Data Fields
Values	vertex_measures
	Stores the scalar curvature measure per indexed vertex element.
Values	edge_measures
	Stores the scalar curvature measure per indexed edge element.
Values	face_measures
	Stores the scalar curvature measure per indexed face element.

Static Public Attributes
static const Dimension	dimension = RealPoint::dimension

Protected Attributes
const SurfaceMesh *	myMeshPtr
	A pointer to the mesh over which computations are done.
Value	myZero
	Zero value for the given type.

Detailed Description

template<typename TRealPoint, typename TRealVector, typename TValue>
struct DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >

Aim: stores an arbitrary measure on a SurfaceMesh object. The measure can be spread onto its vertices, edges, or faces. This class is notably used by CorrectedNormalCurrentComputer and NormalCycleComputer to store the curvature measures, which may be located on different cells. The measure can be scalar or any other summable type (see template parameter TValue).

Description of template class 'SurfaceMeshMeasure'

The common workflow to use this object is to access its public array data with a call to SurfaceMeshMeasure::kMeasures, then resize it and fill in its values. Of course, the indices used to number cells in the SurfaceMesh are the same as the indices used to store the measure associated to cells.

ScalarMeasure mu0( &myMesh, 0.0 );
auto& face_mu0 = mu0.kMeasures( 2 );
face_mu0.resize( myMesh.nbFaces() );
...

Afterwards, you can access the global measure of a set of cells specified by their indices through convenient methods like SurfaceMeshMeasure::vertexMeasure, SurfaceMeshMeasure::edgeMeasure, SurfaceMeshMeasure::faceMeasure, with potential weights.

Template Parameters

TRealPoint	an arbitrary model of RealPoint.
TRealVector	an arbitrary model of RealVector.
TValue	an arbitrary model of CCommutativeRing

Definition at line 82 of file SurfaceMeshMeasure.h.

Member Typedef Documentation

◆ Edge

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef SurfaceMesh::Edge DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::Edge

Definition at line 99 of file SurfaceMeshMeasure.h.

◆ Edges

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef std::vector< Edge > DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::Edges

The type that defines a range of edges.

Definition at line 109 of file SurfaceMeshMeasure.h.

◆ Face

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef SurfaceMesh::Face DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::Face

Definition at line 100 of file SurfaceMeshMeasure.h.

◆ Faces

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef std::vector< Face > DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::Faces

The type that defines a range of faces.

Definition at line 111 of file SurfaceMeshMeasure.h.

◆ Index

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef SurfaceMesh::Index DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::Index

Definition at line 96 of file SurfaceMeshMeasure.h.

◆ RealPoint

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef TRealPoint DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::RealPoint

Definition at line 87 of file SurfaceMeshMeasure.h.

◆ RealVector

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef TRealVector DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::RealVector

Definition at line 88 of file SurfaceMeshMeasure.h.

◆ Scalar

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef RealVector::Component DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::Scalar

Definition at line 102 of file SurfaceMeshMeasure.h.

◆ Self

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef SurfaceMeshMeasure< RealPoint, RealVector, Value > DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::Self

Definition at line 90 of file SurfaceMeshMeasure.h.

◆ Size

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef SurfaceMesh::Size DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::Size

Definition at line 97 of file SurfaceMeshMeasure.h.

◆ SurfaceMesh

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef DGtal::SurfaceMesh< RealPoint, RealVector > DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::SurfaceMesh

Definition at line 95 of file SurfaceMeshMeasure.h.

◆ Value

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef TValue DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::Value

Definition at line 89 of file SurfaceMeshMeasure.h.

◆ Values

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef std::vector< Value > DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::Values

Definition at line 101 of file SurfaceMeshMeasure.h.

◆ Vertex

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef SurfaceMesh::Vertex DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::Vertex

Definition at line 98 of file SurfaceMeshMeasure.h.

◆ Vertices

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef std::vector< Vertex > DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::Vertices

The type that defines a range of vertices.

Definition at line 107 of file SurfaceMeshMeasure.h.

◆ WeightedEdge

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef std::pair< Edge, Scalar > DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::WeightedEdge

Definition at line 104 of file SurfaceMeshMeasure.h.

◆ WeightedEdges

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef std::vector< WeightedEdge > DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::WeightedEdges

Definition at line 113 of file SurfaceMeshMeasure.h.

◆ WeightedFace

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef std::pair< Face, Scalar > DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::WeightedFace

Definition at line 103 of file SurfaceMeshMeasure.h.

◆ WeightedFaces

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef std::vector< WeightedFace > DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::WeightedFaces

Definition at line 114 of file SurfaceMeshMeasure.h.

◆ WeightedVertex

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef std::pair< Vertex, Scalar > DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::WeightedVertex

Definition at line 105 of file SurfaceMeshMeasure.h.

◆ WeightedVertices

template<typename TRealPoint, typename TRealVector, typename TValue>

typedef std::vector< WeightedVertex > DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::WeightedVertices

Definition at line 112 of file SurfaceMeshMeasure.h.

Constructor & Destructor Documentation

◆ SurfaceMeshMeasure()

template<typename TRealPoint, typename TRealVector, typename TValue>

DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::SurfaceMeshMeasure	(	ConstAlias< SurfaceMesh >	aMesh = nullptr,
		Value	zero_value = Value() )

inline

Constructor from mesh.

Parameters

aMesh	any simplified mesh that is referenced in this object.
zero_value	the value 0 for the specified type TValue.

Definition at line 125 of file SurfaceMeshMeasure.h.

127 : myMeshPtr( &aMesh ), myZero( zero_value ) {}

DGtal::SurfaceMeshMeasure

Aim: stores an arbitrary measure on a SurfaceMesh object. The measure can be spread onto its vertices...

Definition SurfaceMeshMeasure.h:83

DGtal::SurfaceMeshMeasure::myZero

Value myZero

Zero value for the given type.

Definition SurfaceMeshMeasure.h:292

DGtal::SurfaceMeshMeasure::myMeshPtr

const SurfaceMesh * myMeshPtr

A pointer to the mesh over which computations are done.

Definition SurfaceMeshMeasure.h:290

Member Function Documentation

◆ edgeMeasure() [1/3]

template<typename TRealPoint, typename TRealVector, typename TValue>

Value DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::edgeMeasure ( const Edges & edges ) const

inline

Parameters

edges any range of (valid) edge indices.

Returns: its measure.

Definition at line 231 of file SurfaceMeshMeasure.h.

    {
      Value m = myZero;
      if ( edge_measures.empty() ) return m;
      for ( auto&& e : edges )  m += edge_measures[ e ];
      return m;
    }

◆ edgeMeasure() [2/3]

template<typename TRealPoint, typename TRealVector, typename TValue>

Value DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::edgeMeasure ( const WeightedEdges & wedges ) const

inline

Parameters

wedges any range of weighted (valid) edge indices.

Returns: its measure.

Definition at line 241 of file SurfaceMeshMeasure.h.

    {
      Value m = myZero;
      if ( edge_measures.empty() ) return m;
      for ( auto&& e : wedges )  m += edge_measures[ e.first ] * e.second;
      return m;
    }

◆ edgeMeasure() [3/3]

template<typename TRealPoint, typename TRealVector, typename TValue>

Value DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::edgeMeasure ( Edge e ) const

inline

Parameters

e	any edge index.

Returns: its measure.

Definition at line 224 of file SurfaceMeshMeasure.h.

    {
      return e < edge_measures.size() ? edge_measures[ e ] : Value();
    }

Referenced by DGtal::SurfaceMeshMeasure< RealPoint, RealVector, Scalar >::measure().

◆ faceMeasure() [1/3]

template<typename TRealPoint, typename TRealVector, typename TValue>

Value DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::faceMeasure ( const Faces & faces ) const

inline

Parameters

faces any range of (valid) face indices.

Returns: its measure.

Definition at line 258 of file SurfaceMeshMeasure.h.

    {
      Value m = myZero;
      if ( face_measures.empty() ) return m;
      for ( auto&& v : faces )  m += face_measures[ v ];
      return m;
    }

◆ faceMeasure() [2/3]

template<typename TRealPoint, typename TRealVector, typename TValue>

Value DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::faceMeasure ( const WeightedFaces & wfaces ) const

inline

Parameters

wfaces any range of weighted (valid) face indices.

Returns: its measure.

Definition at line 268 of file SurfaceMeshMeasure.h.

    {
      Value m = myZero;
      if ( face_measures.empty() ) return m;
      for ( auto&& v : wfaces )  m += face_measures[ v.first ] * v.second;
      return m;
    }

◆ faceMeasure() [3/3]

template<typename TRealPoint, typename TRealVector, typename TValue>

Value DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::faceMeasure ( Face f ) const

inline

Parameters

f	any face index.

Returns: its measure.

Definition at line 251 of file SurfaceMeshMeasure.h.

    {
      return f < face_measures.size() ? face_measures[ f ] : Value();
    }

Referenced by DGtal::SurfaceMeshMeasure< RealPoint, RealVector, Scalar >::measure().

◆ kMeasures() [1/2]

template<typename TRealPoint, typename TRealVector, typename TValue>

Values & DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::kMeasures ( Dimension dim )

inline

Parameters

dim	the dimension of the cells where the measures are defined, among 0: vertex, 1: edges, 2: faces.

Returns: a reference to the dim-measures.

Definition at line 147 of file SurfaceMeshMeasure.h.

    {
      return ( dim == 0 ) ? vertex_measures
        : ( (dim == 1 ) ? edge_measures : face_measures );
    }

◆ kMeasures() [2/2]

template<typename TRealPoint, typename TRealVector, typename TValue>

const Values & DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::kMeasures ( Dimension dim ) const

inline

Parameters

dim	the dimension of the cells where the measures are defined, among 0: vertex, 1: edges, 2: faces.

Returns: a const reference to the dim-measures.

Definition at line 139 of file SurfaceMeshMeasure.h.

    {
      return ( dim == 0 ) ? vertex_measures
        : ( (dim == 1 ) ? edge_measures : face_measures );
    }

◆ measure() [1/2]

template<typename TRealPoint, typename TRealVector, typename TValue>

Value DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::measure ( ) const

inline

Returns: the total measure (i.e. onto the whole space).

Definition at line 161 of file SurfaceMeshMeasure.h.

    {
      Value m = myZero;
      for ( auto&& lm : vertex_measures ) m += lm;
      for ( auto&& lm : edge_measures   ) m += lm;
      for ( auto&& lm : face_measures   ) m += lm;
      return m;
    }

◆ measure() [2/2]

template<typename TRealPoint, typename TRealVector, typename TValue>

Value DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::measure	(	const RealPoint &	x,
		Scalar	r,
		Face	f ) const

inline

Computes the total measure on the ball of center x and radius r. The center x must lie on or close to the face f (as a hint to compute cells in the given ball).

Parameters

x	the position where the ball is centered.
r	the radius of the ball.
f	the face where center point x lies.

Definition at line 176 of file SurfaceMeshMeasure.h.

    {
      if ( vertex_measures.empty() && edge_measures.empty() )
        {
          WeightedFaces
            faces = myMeshPtr->computeFacesInclusionsInBall( r, f, x );
          return faceMeasure( faces );
        }
      else
        {
          std::tuple< Vertices, WeightedEdges, WeightedFaces >
            wcells = myMeshPtr->computeCellsInclusionsInBall( r, f, x );
          Value m = vertexMeasure( std::get< 0 >( wcells ) );
          m      += edgeMeasure  ( std::get< 1 >( wcells ) );
          m      += faceMeasure  ( std::get< 2 >( wcells ) );
          return m;
        }
    }

◆ meshPtr()

template<typename TRealPoint, typename TRealVector, typename TValue>

const SurfaceMesh * DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::meshPtr ( ) const

inline

Returns: a pointer to the associated mesh or nullptr if the measure is not valid.

Definition at line 131 of file SurfaceMeshMeasure.h.

    {
      return myMeshPtr;
    }

◆ vertexMeasure() [1/3]

template<typename TRealPoint, typename TRealVector, typename TValue>

Value DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::vertexMeasure ( const Vertices & vertices ) const

inline

Parameters

vertices any range of (valid) vertex indices.

Returns: its measure.

Definition at line 204 of file SurfaceMeshMeasure.h.

    {
      Value m = myZero;
      if ( vertex_measures.empty() ) return m;
      for ( auto&& v : vertices )  m += vertex_measures[ v ];
      return m;
    }

◆ vertexMeasure() [2/3]

template<typename TRealPoint, typename TRealVector, typename TValue>

Value DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::vertexMeasure ( const WeightedVertices & wvertices ) const

inline

Parameters

wvertices any range of weighted (valid) vertex indices.

Returns: its measure.

Definition at line 214 of file SurfaceMeshMeasure.h.

    {
      Value m = myZero;
      if ( vertex_measures.empty() ) return m;
      for ( auto&& v : wvertices )  m += vertex_measures[ v.first ] * v.second;
      return m;
    }

◆ vertexMeasure() [3/3]

template<typename TRealPoint, typename TRealVector, typename TValue>

Value DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::vertexMeasure ( Vertex v ) const

inline

Parameters

v	any vertex index.

Returns: its measure.

Definition at line 197 of file SurfaceMeshMeasure.h.

    {
      return v < vertex_measures.size() ? vertex_measures[ v ] : Value();
    }

Referenced by DGtal::SurfaceMeshMeasure< RealPoint, RealVector, Scalar >::measure().

Field Documentation

◆ dimension

template<typename TRealPoint, typename TRealVector, typename TValue>

const Dimension DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::dimension = RealPoint::dimension

static

Definition at line 115 of file SurfaceMeshMeasure.h.

◆ edge_measures

template<typename TRealPoint, typename TRealVector, typename TValue>

Values DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::edge_measures

Stores the scalar curvature measure per indexed edge element.

Definition at line 283 of file SurfaceMeshMeasure.h.

◆ face_measures

template<typename TRealPoint, typename TRealVector, typename TValue>

Values DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::face_measures

Stores the scalar curvature measure per indexed face element.

Definition at line 285 of file SurfaceMeshMeasure.h.

◆ myMeshPtr

template<typename TRealPoint, typename TRealVector, typename TValue>

const SurfaceMesh* DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::myMeshPtr

protected

A pointer to the mesh over which computations are done.

Definition at line 290 of file SurfaceMeshMeasure.h.

◆ myZero

template<typename TRealPoint, typename TRealVector, typename TValue>

Value DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::myZero

protected

Zero value for the given type.

Definition at line 292 of file SurfaceMeshMeasure.h.

◆ vertex_measures

template<typename TRealPoint, typename TRealVector, typename TValue>

Values DGtal::SurfaceMeshMeasure< TRealPoint, TRealVector, TValue >::vertex_measures

Stores the scalar curvature measure per indexed vertex element.

Definition at line 281 of file SurfaceMeshMeasure.h.

The documentation for this struct was generated from the following file:

SurfaceMeshMeasure.h

Public Types

Public Member Functions

Data Fields

Static Public Attributes

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ Edge

◆ Edges

◆ Face

◆ Faces

◆ Index

◆ RealPoint

◆ RealVector

◆ Scalar

◆ Self

◆ Size

◆ SurfaceMesh

◆ Value

◆ Values

◆ Vertex

◆ Vertices

◆ WeightedEdge

◆ WeightedEdges

◆ WeightedFace

◆ WeightedFaces

◆ WeightedVertex

◆ WeightedVertices

Constructor & Destructor Documentation

◆ SurfaceMeshMeasure()

Member Function Documentation

◆ edgeMeasure() [1/3]

◆ edgeMeasure() [2/3]

◆ edgeMeasure() [3/3]

◆ faceMeasure() [1/3]

◆ faceMeasure() [2/3]

◆ faceMeasure() [3/3]

◆ kMeasures() [1/2]

◆ kMeasures() [2/2]

◆ measure() [1/2]

◆ measure() [2/2]

◆ meshPtr()

◆ vertexMeasure() [1/3]

◆ vertexMeasure() [2/3]

◆ vertexMeasure() [3/3]

Field Documentation

◆ dimension

◆ edge_measures

◆ face_measures

◆ myMeshPtr

◆ myZero

◆ vertex_measures